Combustion chambers with a closed cooling system for turbines can have walls made, for example, of a hollow tile construction. Known constructions of this kind comprise a central fixing element, a circular feed system and a circular discharge system for a cooling fluid. In such an arrangement, the circular feed system and the circular discharge system for the cooling fluid are separated by means of a rotationally symmetrical flow control body. Because of the intercrossing feed and discharge systems this known form of construction necessitates a very complex design of the outer wall of the combustion chamber.